Inequalities of Ono numbers and class numbers associated to imaginary quadratic fields

Research output: Contribution to journalArticle

Abstract

We denote by hD the class number and by pD the Ono number of the imaginary quadratic fields Q(√-D). Sairaiji-Shimizu [2] showed that there are infinitely many imaginary quadratic fields such that the inequality hD > cpD holds for any real number. On the other hand we have the possibility that hD 5 cpD holds for infinitely many imaginary quadratic fields for the same real number c. In this paper, given a real number c, we consider whether hD 5 cpD holds for infinitely many imaginary quadratic fields or not.

Original languageEnglish
Pages (from-to)46-48
Number of pages3
JournalProceedings of the Japan Academy Series A: Mathematical Sciences
Volume85
Issue number4
DOIs
Publication statusPublished - 2009
Externally publishedYes

Keywords

  • Class number
  • Ono number

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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title = "Inequalities of Ono numbers and class numbers associated to imaginary quadratic fields",
abstract = "We denote by hD the class number and by pD the Ono number of the imaginary quadratic fields Q(√-D). Sairaiji-Shimizu [2] showed that there are infinitely many imaginary quadratic fields such that the inequality hD > cpD holds for any real number. On the other hand we have the possibility that hD 5 cpD holds for infinitely many imaginary quadratic fields for the same real number c. In this paper, given a real number c, we consider whether hD 5 cpD holds for infinitely many imaginary quadratic fields or not.",
keywords = "Class number, Ono number",
author = "Kenichi Shimizu",
year = "2009",
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journal = "Proceedings of the Japan Academy Series A: Mathematical Sciences",
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AB - We denote by hD the class number and by pD the Ono number of the imaginary quadratic fields Q(√-D). Sairaiji-Shimizu [2] showed that there are infinitely many imaginary quadratic fields such that the inequality hD > cpD holds for any real number. On the other hand we have the possibility that hD 5 cpD holds for infinitely many imaginary quadratic fields for the same real number c. In this paper, given a real number c, we consider whether hD 5 cpD holds for infinitely many imaginary quadratic fields or not.

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